The isoperimetric inequality in the n-dimensional Gauss space (namely the n-dimensional Euclidean space endowed with the Gaussian measure) asserts that half-spaces are the unique minimizers of Gaussian perimeter among all subsets of prescribed Gaussian measure. In the present paper we provide a sharp quantitative version of this result. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.
On the isoperimetric deficit in the Gauss space / A.Cianchi; N.Fusco; F.Maggi; A.Pratelli. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - STAMPA. - 133:(2011), pp. 131-186.
On the isoperimetric deficit in the Gauss space
CIANCHI, ANDREA;MAGGI, FRANCESCO;
2011
Abstract
The isoperimetric inequality in the n-dimensional Gauss space (namely the n-dimensional Euclidean space endowed with the Gaussian measure) asserts that half-spaces are the unique minimizers of Gaussian perimeter among all subsets of prescribed Gaussian measure. In the present paper we provide a sharp quantitative version of this result. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.
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